@inbook{3224e350c1fc4bdfa80ca4a62ec3cc89,
title = "A family of unitary operators satisfying a poisson-type summation formula",
abstract = "We consider a weighted form of the Poisson summation formula. We prove that under certain decay rate conditions on the weights, there exists a unique unitary Fourier-Poisson operator which satisfies this formula. We next find the diagonal form of this operator, and prove that under weaker conditions on the weights, a unique unitary operator still exists which satisfies a Poisson summation formula in operator form. We also generalize the interplay between the Fourier transform and derivative to those Fourier-Poisson operators.",
author = "Dmitry Faifman",
year = "2012",
doi = "https://doi.org/10.1007/978-3-642-29849-3_11",
language = "الإنجليزيّة",
isbn = "9783642298486",
series = "Lecture Notes in Mathematics",
pages = "191--204",
booktitle = "Geometric Aspects of Functional Analysis",
}